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Full text of "Effect of configuration variables on performance of solid fuel ramjets."

EFFECT OF CONFIGURATION VARIABLES 
ON PERFORMANCE OF SOLID FUEL RAMJETS 



Clemens James Mady 



WttFt WWX U8RARY 
NAVAL POSTGRADUATE SCHOOl 



NAVAL POSTGRADUATE SCHOOL 

Monterey, California 




THESIS 



EFFECT OF CONFIGURATION VARIABLES 
ON PERFORMANCE OF SOLID FUEL RAMJETS 



by 



Clemens James Mady, Jr. 



June 1977 



Thesis Advisor: 



David W. Netzer 



Approved for public release; distribution unlimited 



T1800 



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REPORT DOCUMENTATION PAGE 


READ INSTRUCTIONS 
BEFORE COMPLETING FORM 


t. REPORT NUMBER 


2. GOVT ACCESSION NO. 


3. RECIPIENT'S CATALOG NUMBER 


4. TITLE (and Subtitle) 

Effect of Configuration Variables on 
Performance of Solid Fuel Ramjets 


5. TYPE OF REPORT & PERIOD COVERED 

Master's Thesis; June 1977 


8. PERFORMING ORG. REPORT NUMBER 


7. AUTHOR^*; 

MADY, Clemens James, Jr. 


8. CONTRACT OR GRANT NLMBERf*; 

77WR30051 


9. PERFORMING ORGANIZATION NAME AND ADDRESS 

Naval Postgraduate School 
Monterey, California 93940 


10. PROGRAM ELEMENT, PROJECT. TASK 
AREA & WORK UNIT NUMBERS 


11. CONTROLLING OFFICE NAME AND ADORESS 

Naval Postgraduate School 
Monterey, California 93940 


12. REPORT DATE 

June 1977 


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U. MONITORING AGENCY NAME a AOORESSf/f dlttarant trom Controlling Ottlca) 

Naval Postgraduate School 
Monterey, California 93940 


IS. SECURITY CLASS, (ot thia riport) 

Unclassified 


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SCHEDULE 


16. DISTRIBUTION STATEMENT (ol thia Raport) 

Approved for public release; distribution unlimited. 


17. DISTRIBUTION STATEMENT (of tha abstract antarad in Block 20, II dlttarant from Raport) 


IB. SUPPLEMENTARY NOTES 


19. KEY WORDS (Contlnua on ravaraa alda It nacaaaary and Idanttty by block numbar) 

Ramjet, Solid Fuel, Performance 


20. ABSTRACT (Contlnua on ravaraa alda It nacaaaary and Idanttty by block numbar) 

An experimental investigation into the effect of configuration 
variables on combustion performance in the solid fuel ramjet was conducted. 
The effect of air ducting methods on combustion efficiency was found to be 
dependent not only on the flow rates, momentum and geometry of the system but 
also on the composition of the solid fuel. High pressures and lew air 
mass fluxes through the fuel grain affect the regression rate by altering 



DD 



FORM 
1 JAN 73 



1473 EDITION OF 1 NOV 88 IS OBSOLETE 

S/N 0102-014- 6801 i 



SECURITY CLASSIFICATION OF THIS PAGE (Whan Data Kntarad) 



fuCtjmTV CL ASSiyiCATlON Of TMIS P«Otr*lnB D»c« fni.r.J 



20. the heat transfer mechanism. Some air duct configurations were 
found to create a favorable environment for combustion pressure 
oscillations . 



DD Form 1473 

1 Jan 73 

w, N 0102-014-6601 9 SECURITY CLAUl'lCATION O^ THIS ^»Gtr»*«n D«»« ?nf«r«dj 



Approved for public release; distribution unlimited 



Effect of Configuration Variables on Performance of Solid 

Fuel Ramjets 



by 



.y, Jr. 

it! ' 



Lieutenant, United States Navy 
B.S., United States Naval Academy, 1970 



Submitted in partial fulfillment of the 
requirements for the degree of 



MASTER OF SCIENCE IN AERONAUTICAL ENGINEERING 

from the 
NAVAL POSTGRADUATE SCHOOL 
June 1977 






ABSTRACT 



An experimental investigation into the effect of 
configuration variables on combustion performance in 
the solid fuel ramjet was conducted. The effect of 
air ducting methods on combustion efficiency was found 
to be dependent not only on the flow rates, momentum 
and geometry of the system but also on the composition 
of the solid fuel. High pressures and low air mass 
fluxes through the fuel grain affect the regression 
rate by altering the heat transfer mechanism. Some 
air duct, configurations were found to create a 
favorable environment for combustion pressure 
oscillations. 



TABLE OF CONTENTS 



I. INTRODUCTION 8 

II. METHOD OF INVESTIGATION 12 

III. DESCRIPTION OF APPARATUS 13 

A. RAMJET MOTOR 13 

B. IGNITION SYSTEM 16 

C. NITROGEN PURGE AND COOLING AIR SYSTEM... 16 
C. AIR FLOW CONTROL 16 

E. DATA ACQUISITION SYSTEM 17 

F. AIR FEED SYSTEM 17 

IV. EXPERIMENTAL PROCEDURE 19 

V. RESULTS AND DISCUSSION 22 

A. DATA REDUCTION METHODS 22 

E. REGRESSION RATE 24 

C. COMBUSTION EFFICIENCY 27 

D. COMBUSTION PRESSURE OSCILLATIONS 31 

VI. CONCLUSIONS 33 

VII. SUGGESTIONS FOR FUTURE WORK 35 

Appendix A: RAMJET DATA 47 

Appendix 3: THEORETICAL PERFORMANCE FOR PMM-AIR. . . 52 

LIST OF REFERENCES 54 

INITIAL DISTRIBUTION LIST 56 



LIST OF FIGURES 

1. Solid Fuel Ramjet Motor 36 

2. Schematic of Solid Fuel Ramjet Apparatus 37 

3. Raajet Motor on Test Stand 38 

4. Test Stand 39 

5. Test Stand 40 

6. Raajet Motor Firing 41 

7. Regression Rate-Non Bypass 42 

8. Regression Rare-Bypass 43 

9. Combustion Efficiency vs. Air Flux Rate 44 

10. Combustion Efficiency vs. Bypass Ratio 45 

11. Regression Rate vs. Bypass Ratio 46 



ACKNOWLEDGEMENTS 

The author wishes to express his appreciation to 
Associate Professor David W. Netzer of the Department of 
Aeronautics for his guidance, encouragement and assistance 
throughout the project. 

Appreciation also goes to Patrick J. Hickey, Jr., 
Glen Middleton and Frank Abbe, who with the remainder of the 
technical staff of the Aeronautics Department furnished 
timely and efficient technical assistance. 

This work was sponsored by the Naval Weapons Center, 
China Lake, California under Work Request number 77WR30051. 



I. INTRODUCTION 

Several characteristics of the solid fuel ramjet 
indicate that it may be superior to other forms of 
propulsion for tactical weapons used at intermediate ranges 
and high speed. Having no moving parts, the solid fuel 
ramjet is simple and relatively inexpensive to fabricate. 
Weight of the system and its threat as a fire hazard are 
both decreased by use of the solid fuel. 

To be used in a tactical situation, the solid fuel 
ramjet has to demonstrate combustions stability and 
efficiency over the expected operating envelope of altitudes 
and Mach numbers. It must also show performance comparable 
to that of liquid fuel ramjets and ducted rockets. 

Combustion studies on the solid fuel ramjet have been 
underway at United Technologies-Chemical Systems Division 
( Ref. 1 ) since 1971. Initial work showed low temperature 
rise combustion efficiencies. The discovery of the rearward 
facing step at the combustor entrance as a flameholder was a 
significant step in solid fuel ramjet technology. Overall 
performance, however, was reduced by the high stagnation 
pressure loss produced by the rearward facing step. Further 
work by United Technologies in the field of flame 
stabilization involved various inlet designs including 
aerogrids, distorted flows, non-circular inlets and vortex 
generators. This effort has led to the development of low 
pressure loss inlets which appear to have minimized inlet 
step height requirements and eliminated most inlet distor- 
tion effects on flame holding. 



stabilization, thereby reducing the pressure loss through 
the injector. 

Work was also underway at the Naval Postgraduate School 
on the internal ballistics of the solid fuel ramjet. Jones 
and Netzer ( Ref. 2 ) showed that inlet turbulence and 
distortion may have a significant effect on flame stability. 

The solid fuel ramjet, which uses air as the oxidizing 
agent, is similiar to the hybrid rocket and has two distinct 
combustion zones ( fief. 3 ) . Behind the step is the 
recirculation zone where an intense mixing of reactants and 
products takes place. The hot products ignite the reactants 
and combustion may in the limiting case approach that of a 
well-stirred reactor. This combustion region acts as the 
flame initiator for the combustion which takes place further 
down the fuel grain. 

Downstream of the flow reattachment point a boundary 
layer develops. Here combustion is similiar to that of the 
hybrid rocket. A diffusion flame exists in the boundary 
layer between the fuel rich zone near the wall and the 
oxygen rich central air core. Heat is transported by 
convection and radiation to the solid surface which causes 
decomposition of the fuel. Studies have shown the rate of 
decomposition of the fuel is sensitive to the combustion 
pressure and the mass flux of the air. 

The combustion process in the solid fuel ramjet is 
thought tc be mixing limited at combustion pressures greater 
than 10-15 psia for all-hydrocarbon fuels ( Ref. 4 ) . 
However, this remains to be verified and other fuels have 
demonstrated behavior more characteristic of kinetically 
controlled combustion. [Jnburned gaseous fuel escapes from 
under the flame at the aft end of the fuel grain and results 
in decreased combustion efficiency. Temperature rise 



efficiencies based on both thrust and pressure measurements 
were found to be correlated by parameters reflecting the 
rate of mixing. Work by United Technologies showed that 
combustion efficiency can be improved by increasing the rate 
of mixing between the fuel rich boundary layer and the 
central air core. However, too rapid mixing may quench the 
reaction and further reduce combustion efficiency. 

Work at the Naval Weapons Center, China Lake ( Ref. 5 ) 
and at United Technologies ( Ref. 4 ) has further shown that 
combustion is increased with the use of an aft mixing 
chamber. Intense combustion with strong gas temperature 
increases ware observed for L/D ( length to diameter of 
mixer ) ratios up to 3.3. 

The use of aft-end mixing devices to improve combustion 
efficiency is an area of recent interest in solid fuel 
ramjet technology. As another means of promoting mixing, 
the bypassing of a portion of the inlet air around the fuel 
grain and dumping it into the aft mixing chamber is being 
re-evaluated. A meteorlogical sounding rocket capable of an 
altitude of 200,000 feet was designed and built by Anderson, 
Greenwood and Co., Houston, Texas in 1961 ( Ref. 6 ) . The 
MET JET employed a ramjet using a magnesium and 
magnesium-aluminum alloy epoxy-metal charge. Eighty-five 
percent of the inlet air was bypassed around the fuel grain 
to mix in an afterburner section with the fuel rich primary 
flow. 

In the bypass systems, the flow rates into the fuel 
grain inlet and aft mixing section are critical factors in 
determining combustion efficiency. Bypass air flow of too 
low a percentage of the total air mass flow or of toe low 
momentum may have negligible effect on the combastion 
efficiency. Bypass air of too high a flow rate or momentum 
may have a negative effect on the combustion process. The 



10 



bypass air is of appreciably lower temperature than the 
species which exit from the fuel grain, and air injected at 
too high a rate may cool the process sufficiently to affect 
the kinetics of the reaction. Furthermore, the combustion 
process in the aft mixing chamber may also be a function of 
the axial and radial positions and of the angular 
orientations of the aft dumps. 

This research was concerned with the use of bypass air 
flow as a means of improving combustion efficiency. Mass 
flew rate, momentum, and the number, location and angular 
orientation of the aft dumps and the use of an orifice plate 
between the fuel grain and aft mixing chamber were evaluated 
to determine their effects on the combustion process. 

Polymethylmethacrylate (PMM) was used as a fuel in this 
research. PMM becomes a monomer in the gaseous phase while 
currently used hydrocarbon fuels are polymers. 



11 



II. METHOD OF INVESTIGATION 



Experimental firings of the solid fuel ramjet were 
conducted using polymehtylmethacryla te fuel grains while 
varying primary-to-bypass air flow ratios and aft dump 
geometry. The tests were performed to provide data for the 
study of the effect of bypass air flow on combustion 
efficiency. 



12 



III. DESCRIPTION OF APPARATUS 



RAMJET MOTOR 



The solid fuel ramjet motor ( Fig. 1 ) , with the 
exception of the bolts, was made of stainless steel. The 
first two sections, the head end assembly and the step 
insert section, were those previously used by Boaz and 
Netzer ( Ref . 3 ) . The other two sections were the fuel 
grain and the aft mixing section. 

The head end assembly contained the inlet to the ramjet 
motor and the ports for the ignition system oxygen and 
methane. Also in the assembly were mounted the two Champion 
Z7 spark plugs used in the ignition system, an 
iron-constantan thermocouple to measure inlet air 
temperature and a pressure tap connected to a Wiancko 0-200 
psig pressure transducer to measure inlet pressure. 

The step insert section held an insert with an inside 
diameter of .50 inches and was also used for mounting the 
front end of the fuel grains. 

The fuel grains were made of Polymethylmethacrylate, 
chosen oecause of its previous use in the study of internal 
ballistics of solid fuel ramjets at the Naval Postgraduate 
School and because it facilitates flame observation. 



13 



PMM is a polymer of the form: 



H 



H 



CH. 



COOCH. 



The stoichicmetric equation for complete combustion with 
air is: 



C 5 H 8°2 + 60 2 + 22 ' 5N 2 "* 4H 2° + 5C0 2 + 22 - 56N 2 



The theoretical equilibrium composition and temperature for 
combustion at different air-fuel ratios, inlet air 
temperatures and combustion pressure were obtained from the 
Naval Weapons Center, China Lake, California. 

The PMM was cut into fuel grains 12 inches long and 3.75 
inches square. The front and rear of the grains were 
machined to an outside diameter of 3.50 inches to fit into 
the step insert and aft mixing sections where "0" rings were 
used for the seal. With the exception of one run, all grains 
were bored to an inside diameter of 1.50 inches. This 
provided an air injector step height to grain port diameter 
ration, h/D, of 0.333 (or equivalently a port to injector 
area ratio of 9.0 ) . 

The aft mixing section fit to the rear of the grain and 
was tied to the step insert section with four 3/8-inch steel 



14 



rods. The mixer was 6.22 inches long and had an (L/D) 

mixer 

of 2. 93. It was comprised of five sections to facilitate the 
changing of design variables. The first section, 1.688 
inches in length, was used to mount the mixer to the grain 
and to hold the mixing orifice plate. The plate had an 
outside diameter of 3.0 inches and an inside diameter of 
1.50 inches, and when installed provided a constant 

L /D for flow into the mixing section, 
mixer port 

The second section was 2.0 inches long and contained the 
four inlets for the secondary or bypass air flow. The inlet 
diameters were 1.063 inches with plugs available to reduce 
the diameters to 0.813, 0.751, 0.574 or 0.25 inches, or -co 
seal the inlets off entirely. 

The third section, also 2.0 inches long, was used in 
conjunction with the second section to alter the axial 
position cf the bypass air inlets. 

The fourth section, 1.433 inches in length, contained 
two pressure taps located 180 degrees apart which were 
connected to a Wiancko 0-150 psig pressure transducer to 
measure combustion pressure. 

The last section of the aft mixer was the end plate 
containing the converging-diverging nozzle. The nozzle 
consisted of a circular arc converging section, a straight 
throat section of constant diameter and a conical exit 
section with a half angle of 30 degrees. The nozzle throat 
diameter was 0.75 inches, which provided a port- tc- throat 
diameter ratio of 4.0. 

The aft mixing section was held together by four 3/8 
inch stainless steel rods with "0" ring seals between the 



15 



individual sections and was supported by a mounting flange 
on the test stand. 



B. IGNITION SYSTEM 



Oxygen and methane in two high pressure tanks were 
delivered at 700 psig through two needle valves to inlet 
ports in the head end assembly. A Model T ignition coil and 
transformer supplied the spark to the two Champion Z7 spark 
plugs located downstream of the inlet ports. 



C. NITROGEN PURGE AND AIR COLLING SYSTEM 



To extinguish the flame at the end of a firing, nitrogen 
was fed momentarily into the system (upstream of the head 
assembly section) from two high pressure bottles at 80 psig 
The motor was then cooled with air from a low pressure com- 
pressor. 



D. AIR FLOW CONTROL 



Aif flow rates through the primary and bypass lines were 
measured by two standard ASME orifices. The primary had 
flange taps and the bypass had taps at 1 D and 1/2 D. 
Primary and bypass flows were controlled by manually 
operated valves. Primary air was either vented to the 
atmosphere or routed through the motor by two pneumatically 
operated Jamesbury ball valves working together. Bypass air 
was continually passed through the aft mixing section. 



i fi 



E. DATA ACQUISITION 



Temperatures at the orifices and the inlet ro the motor 
were measured by iron-constantan thermocouples and recorded 
on a 0-600°F strip chart, recorder. 

The upstream pressure of the primary orifice was 
measured by a 0-500 psig Taber pressure transducer while a 
0-200 psig Wiancko pressure transducer was connected 
upstream of the secondary orifice. Colvin 0-35 psi 
differential pressure transducers were used to measure the 
pressure drops across the two orifices. The inlet pressure 
to the motor was measured by a 0-500 psig Wiancko pressure 
transducer, and a 0-120 psig Wiancko pressure transducer was 
used to measure the chamber pressure in the aft mixing 
section. 

All transducer outputs, along with a 5 cycle per second 
timing signal and an ignition pulse, were connected to a 
Honevwell Model 2106 Visicorder. 



AIR FEED SYSTEM 



A Pennsylvania air compressor capable of 700 scfm 
supplied air at a pressure of 150 psia. A portion of this 
air was routed through the heat exchanger of a Polytherm air 
heater and provided non-vitiated hot air. The air heater 
had a capability of 1.75 pounds per second at 150 psia and 
1000°?. 

Two valves and a temperature controller mixed the hot 
air with the remaining cold air to supply air at the desired 
temperature. Air flow was controlled by a manual gate valve 



17 



before leaving the pump room. In the test cell the flow of 
air was controlled by an electrically operated gate valve 
before being split into primary and secondary air flows 
upstream cf the orifice flow meters. Figure 2 presents a 
schematic of the test apparatus. Figures 3 through 6 present 
photographs of the ramjet motor and test stand. 



18 



IV. EXPERIMENTAL PROCEDURE 



All test firings were performed in the jet engine test 
cell at the Naval Postgraduate School. Data for calculating 
temperature rise efficiencies based on combustion pressure 
were obtained while varying primary and bypass air flow 
rates and bypass dump geometry. Nominal air flow rates were 
0.1 and 0.2 lbm/sec for non-bypass runs and 0.2 lbm/sec for 
runs using bypass. In the bypass runs, primary-to-bypass 
air flow ratios employed were 65/35, 50/50 and 35/65. 

Two and four aft dumps, ranging in diameter from 0.25 to 
1.063 inches, were used. Dump size was varied to allow 
different total and individual air flow momentum in the aft 
dumps. Momentum relations for all tests were compared to a 
reference condition which used a bypass air flow rate of 0.1 
lbm/sec and two dumps with diameters of 0.313 inches. 

With the exception of the runs using swirl, all dumps 
were oriented perpendicular to the centerline of the aft 
mixer. With swirl, the dumps were oriented to inject the 
air flow tangentially to the circumference of the mixer. 
Tast firings through run no. 3 were made without the aft 
orifice mixing plate. The remaining runs ( beginning with 
no. 9 ) all used the aft orifice. 

Tests were conducted with the dump section in both 
positions two and three of the aft mixing chamber to observe 
the effect of air injection prior to and after the predicted 
primary flow reattachment point ( Ref . 7 ) . 



19 



The nozzle for all PMM firing runs had a diameter of 

0.75 inches. For the expected combustion temperatures and 

planned air flow rates, this nozzle kept the combustion 

pressure low enough to maintain choKed flow across the 
upstream air flow control valve. 

The majority of the test firings were made using a 
nominal inlet air temperature of 70°F. For those using the 
Polytherm air heater, two to three hours were allowed for 
the temperature to stabilize at the ramjet inlet and in the 
bypass air line. The low flow rates to the motor 
necessitated this delay. 

The weight, length and inside diameter of the fuel 
grains were measured prior to being mounted in the motor. 
The ignition sequence normally lasted for six seconds. An 
average of three seconds was required for the ignition flame 
to propagate from the head end assembly into the fuel grain. 
After five seconds, the air was directed through the ramjet 
motor. Ignition was continued into the first second of the 
run to insure that combustion would be sustained. Total 
time of the ignition flame in contact with the fuel grain 
amounted to approximately three seconds. Two tests were 
made using only the ignition system in order to determine 
the rate of consumption of the PMM grains during the 
oxygen-methane ignition. These data were used to correct 
the initial weight of the fuel used in the efficiency 
calculation. 

Combusticn normally lasted for forty-five seconds. The 
motor was extinguished at the end of each run by 
siniultanecuely venting the air to the atmosphere with the 
Jamesbury ball valves and actuating the nitrogen purge 
system. Lew pressure air was then blown through the motor 
for cooling. After a sufficient period of time, the fuel 



20 



grain was removed and the final weight and aft end inside 
diameter were measured. 



21 



V. RESULTS AND DISCUSSION 



A. DATA REDUCTION METHODS 



Thirty-three hot firing PMM tests were conducted. 
Measured and reduced data for the runs in which combustion 
was sustained are tabulated in Appendix A. 

Data reduction was accomplished on the Hewlett-Packard 
9830 using a basic language program. Combus-cion 
efficiencies were based on the total temperature rise from 
just upstream of the rearward facing step to the aft mixing 
ssction ( Ref . 8 ) . Inlet total temperature was derived 
from the measured inlet static temperature. 

Polynomial regressions were performed on the data from 
the Naval Weapons Center, China Lake. Equations for the 
ideal combustion temperature, gas constant and ratio of 
specific heats based on equilibrium calculations are 
presented in Appendix 3. 

Actual combustion temperature was derived from the 
measured static pressure in the aft mixer. With choked flow 
across the exit nozzle, the mach number in the mixing 
section was obtained from the isentropic relation for A/A*. 
With the air ana fuel flow rates, Mach number and pressure 
knewn in the aft mixer, combustion temperature was 
calculated using the continuity equation. 



22 



The stagnation pressure in the aft mixing section was 
derived from the measured static pressure and was used to 

calculate the actual C . Ideal C was calculated using the 

ideal combustion total temperature. C efficiency, is the 

ratio of the actual to ideal C . 

The actual composition of the exit products of the SFRJ 
are unknown. To obtain a more realistic value for the 
efficiency cf the motor, a second calculation of 
efficiencies was performed. It was assumed that 
inefficiency in the SFRJ combustion was due to incomplete 
combustion and therefore the species that would be present 
from complete combustion were only present in a percentage 
equal to the initially calculated efficiency. The remaining 
fraction cf exit products was assumed to be comprised of 
unreacted air and fuel in a percentage equal to the air-fuel 
ratio. Based on this assumption, a new average molecular 
weight for the combustion products and a new gas constant 
were computed. This new value was then used to re-calculate 
the efficiencies. This resulted in a higher average 
molecular weight and higher efficiencies. Both values for 

* 
the temperature rise combustion efficiencies and the C 

efficiencies are included in Appendix A. Further data 
reductions, correlations and discussions were based on the 
corrected coiibustion efficiency. 

Regression rate was calculated based on weight loss of 
the fuel. The inside diameter of the aft end of the fuel 
grain was also measured before and after each firing. 
However, as with Eoaz and Netzer ( Ref . 3 ) , it was found 
that weight loss gave a better value of regression rate than 



23 



the method based on aft end diameter change, due tc the 
non-uniform regression along the length of the grain. 

The expected uncertainties in the experimental results 
were calculated using the method of Kline and McClintock 
( fief. 9 ). These uncertainties are given in Table I. 



B. REGRESSION RATE 



Several runs were made without using bypass air. These 

showed the dependence of the regression rate, f (in/sec) on 

combustion pressure, P (psia) and average mass flux of air, 

2 
G (lbm/in -sec) to be: 

.29 .38 
f = .0043P G (1) 

A plot- cf the regression rate versus this emperical 
regression rate equation for the 0.2 and 0.1 lbm/sec 
non-bypass runs made with cold inlet air is shown in Figure 
7. 

In their work with PMM, Boaz and Netzer ( Ref. 3 ) had 
shown a regression rate dependence of the form: 

.51 .34 .41 
f = CP T G (2) 

where C is a constant and T is the inlet air temperature. 

Insufficient runs were made in this investigation at 
other than ambient inlet temperature to calculate a 
temperature dependence for the regression rate. The above 
equations for regression rate agree closely for the 
dependence on G. The dependence on pressure was 
significantly less in this study. In the work of Boaz and 



24 



TABLE I 



ERROR ANALYSIS 



Variable 



Percent Error 



Air Weight Flow Rate 
Fuel Weight Flow Rate 
Air Flux Rate 
Combustion Efficiency 
Regression Rate 

C Efficiency 

Actual Combustion Temperature 

Ideal Combustion Temperature 



1. 1 

0.4 
1.2 
7.0 
1.2 

2.3 
5.6 
1.7 



25 



Netzer, chamber pressure was varied intentionally from 37 to 
108 psia by varying the throat size. In this study pressure 
varied between 33 and 63 psia only as a result of varying 
combustion efficiency and G. 

With the application of bypass air, the dependence of 
regression rate on pressure and air flux rate was altered. 
In figure 8 are plotted the cold 0.2 lbm/sec non-bypass 
cases and the bypass runs made with 0.2 lbm/sec total air 
flow rate and individual dump momentum equal to that of the 
reference condition. The reference condition, as described 
in the chapter on Experimental Procedure, is a bypass air 
flow rate of 0.1 lbm/sec and two dumps with diameters of 
0.813 inches. This corresponds to a dump momentum to fuel 
grain port momentum ratio of approximately 0.5. A slightly 
stronger dependence on pressure was shown, while regression 
rate indicated very little or no dependence on air flux rate 
for the values tested. Here regression rate took the form: 

.42 .003 
f = .00116P G (3) 

In the bypass situation, the mass flux through the grain 
is low but the pressure is maintained high due to the total 
mass flux through the nozzle throat. However, correcting 
the regression rate for the increased pressure per equation 
(2) does nor result in regression rates as high as the 
experimental data. In addition, regression rates based on 
weight and diameter agree, indicating that the change does 
not result from different comoustion behavior within the aft 
mixing chamber. These conditions of low G and hign P 
minimize the convective heat flux to the fuel surface but 
maximize radiative heat flux. Thus, the regression rate 
becomes sensitive to pressure and mixture ratio. PMM-Air 
combustion at the high air mass fluxes has both radiative 
and convective transfer to the surface as indicated by 
equation (1). However, the pressure dependence could also 



26 



result from kinetic controlled combustion. For the bypass 
situation, PMM-Air combustion appears to become dominated by 
radiative heat transfer as indicated by equation (3) . For 
lower G the regression rate increases relative to the air 
flux, i.e., more unburned fuel exists within the fuel grain 
underneath the diffusion flame within the thicker boundary 
layer; Thus, more gas with radiative properties is present. 



C. COMBUSTION EFFICIENCY 



The effects of air mass flux and bypass ratio separately 
on combustion efficiency were then studied to determine the 
overall effect of bypass air flow on combustion performance. 

In Figure 9 are plotted the cases from both Figures 7 
and 8. As can be seen from this figure and the data of 
Appendix A, the use of bypass air flow in a solid fuel 
ramjet using Polymethylmethacrylate as a fuel has the effect 
of reducing combustion performance. For the non-bypass 
runs, a decrease in air flow brings a decrease in combustion 
efficiency. While maintaining the same air flux through the 
grain, injecting bypass air into the mixing section brings a 
further decrease in performance. Decreasing or increasing 
air flux through the fuel grain while maintaining the same 
total flow rate in the bypass case also brings about a 
corresponding change in combustion efficiency. 

The same conclusion can be drawn from the study of 
efficiency as a function of bypass ratio. To prevent 
singularities in the multiple regression analysis of the 
data, the bypass ratio was defined as the ratio of primary 
air mass flow rate to the total air mass flow rate. An 
increase in bypass ratio in this study means an increase in 
the percentage of air flow through the fuel grain and a 



27 



decrease in the percentage of air flow through the aft 
mixing dumps. 

As indicated by Figure 10, which again plots the cold 
0.2 lbm/sec non-bypass cases and the 0.2 lbm/sec reference 
bypass momentum cases, increasing the percentage of total 
air flow through the fuel grain brings an increase in 
combustion efficiency. The oes-t performance occurs in the 
limiting case of all of the air flow through the grain and 
no bypass. 

Figure 11 shows a correlation between regression rate 
and the bypass ratio. The increase in regression rate was 
expected, as an increase in bypass ratio results in both an 
increase in air mass flux through the fuel grain and an 
increase in combustion pressure. 

To further study the decrease in performance found when 
using bypass, other test conditions were considered. Runs 5 
and 7 were run with the dumps located behind the aft mixing 
chamber reattachment point. There was only a slight 
decrease in combustion efficiency (81.2%) over that of 
identical runs in the forward position (83.0%). This 
difference is negated by the possible experimental error 
involved in calculating combustion efficiency. In fact, it 
should be mentioned that temperature rise efficiencies based 
on pressure are prone to error, since uncertainty in 
efficiency goes as the square of the uncertainty in the 
pressure measurement. 

Three runs were made varying the momentum of the 
individual dumps from the reference condition. Small 
changes in momentum had no effect. Varying the momentum 
frcm 0.5 (run 17) to 2.0 (run 24) gave efficiencies of 82.5% 
to 82.8% compared to a reference run efficiency of 83.03. 
However, when a significantly large increase in momentum was 



28 



effected (run 29) , the combustion performance showed a 
noticeable decrease (72.8%). 

Only limited data were taken (runs 18,19,20) for other 
than two dumps at 180 degrees. However, the data showed 
that with low momentum . two or four dumps spaced 9 
degrees circumferentially reduced the combustion efficiency. 
Four ninety degree dumps with high momentum did not change 
the combustion efficiency significantly. 

The last variation in geometry studied was the use of 
swirl on the aft dump process. This was accomplished by 
injecting the dump air with a tangential velocity component. 
The solid fuel ramjet motor was run without fuel grain 
ignition, both with and without swirl, to determine the 
effect of the induced vorticity on the effective exit nozzle 
diameter. Decreasing the effective nozzle diameter would 
increase the combustion chamber pressure and give false 
indications of higher efficiency. The swirl was found to 
not affect the effective throat diameter. Two test firing 
runs were made with swirl, giving an average combustion 
efficiency of 86.4% and the highest performance of any 
bypass firing run. 

Every form of bypass used showed a decrease in 
combustion performance. This indicates that the decrease in 
performance is due to the effect of the bypass air flow on 
the kinetics of the combustion process within the aft mixing 
chamber. An analysis of the effects can lead to a better 
understanding of the internal ballistics in the aft mixing 
chamber. Equal decreases in performance were reached with 
the dump air injected both behind and in front of the 
reattachment point. This indicates that there is a 
significant amount of the combustion process still taking 
place downstream of the reattachment point in the aft mixing 
chamber. This agress with the temperature data presented by 



29 



Schadow ( Ref. 10 ) for an all-hydrocarbon fuel. In the 
case of PMM, the light weight unburned hydrocarbons that 
enter the aft mixing chamber apparently burn most completely 
when allowed to react slowly with the available oxygen in 
the hot flow through the core of the fuel grain. 

The possibility of the temperature of the air entering 
the aft mixer causing reduced combustion efficiency was 
considered. In run number 9 the temperature entering both 
the grain and aft mixer was increased from approximately 
520°R to 705°R. The combustion efficiency did not change 
significantly, indicating that for ?MM-Air combustion the 
dump air temperature is probably not as important as the 
guantity and temperature of the unburned fuel and the mixing 
rate. 

In the region in front of the reattachment point, the 
less that was done to disturb the flow resulted in better 
performance. In the case of swirl, where the bypass flow 
remained close to the wall and within the recirculation 
zone, bypass efficiency was maximized. When the bypass 
momentum was increased to where the flow disturbed the fuel 
rich layer between the recirculation region and the air rich 
central cere, performance decreased. This again indicates 
that a major portion of the combustion process takes place 
along this fuel rich layer or that the process downstream is 
highly dependent on the high temperatures in this layer. It 
also indicates that the combustion mechanisms around this 
layer are more important than those which occur within the 
recirculation region. 

Although the use of Polymethylmethacrylate as a fuel in 

a solid fuel ramj.et using bypass has net shown an increase 

in performance, it has given evidence as to the internal 
combustion processes within an aft mixing chamber. 



30 



It is known that the use of bypass improves performance 
in solid fuel ramjets using all-hydrocarbon fuels. In the 
case of oxygen-containing fuels and for fuels which 
decompose into monomers or small hydrocarbon molecules (such 
as PMM) , results indicate that the fuel burns most 
efficiently without bypass. 

The use of bypass systems has meant an increase in 
weight, cost and complexity of the solid fuel ramjet. In 
addition, they may introduce combustor-f eed system coupling. 
The use of a fuel which has sufficient density impulse, 
regression rate and flammability limits to minimize inlet 
total pressure losses has led to the use of all-hydrocarbon 
fuels. Although PMM does not meet the criteria for a good 
fuel, the results of this study indicate that future fuel 
studies may be fruitful if directed toward ones which 
contain low percentages of oxidizer and/or substances which 
unzip the hydrocarbon chain. 



D. COMBUSTION PRESSURE OSCILLATIONS 



In the non-bypass test runs, the inlet and combustion 
pressures exhibited a steady, small amplitude (approximately 
2% of chamber pressure) oscillation of approximately 150 Hz. 
In the bypass runs of reference condition momentum, the same 
oscillaticn appeared though of considerably higher amplitude 
(approximately 30% of chamber pressure) . Computations made 
from the dimensions of the ramjet motor and the associated 
ducting indicated that this oscillation was probaaly not a 
combustor-f eed system instability. 

In the cases of low or very high aft dump momentum, a 
second oscillation appeared along with that previously 
mentioned.. This oscillation was of very low frequency 



31 



(1 Hz.) and large amplitude (approximately 20% of chamber 
pressure) and may be connected with behavior within the 
mixing chamber recirculation zone. It is possible that the 
aft dump process slows the reaction in the fuel rich shear 
layer passing by th-e recirculation zone (by direct mixing, 
displacement of the entire recirculation zone or increased 
mixing between the fuel and air exiting the fuel grain) . 
When this happens, combustion pressure could drop, followed 
by a decrease in regression rate. Then, as the mixture 
ratio in the shear layer becomes closer to stoichiometric, 
the reaction rate and temperature would increase, causing an 
increase in combustion pressure. This pressure increase 
would increase the regression rate to complete the cycle. 
This mechanism is guite speculative and others are equally 
plausible. However, the bypass-generated very low frequency 
pressure oscillations do appear to be coupled to the fuel 
regression rate. 



32 



VI. CONCLUSIONS 



The use of bypass air flow in the solid fuel ramjet has 
a significant effect on combustion performance. Air flow 
injected into the aft mixing chamber has a more pronounced 
effect on the combustion process when a high enough momentum 
is provided for the bypass air to reach the fuel rich shear 
layer trailing from the port of the fuel grain. Bypass air 
which remains in the recirculation zone also effects 
combustion, but not to as great an extent. 

A significant amount of combustion occurs downstream of 
the reattachment point. This is evidenced by the effect of 
bypass air injected into this region, and is supported by 
data from previous work done on flows in aft mixing 
chambers . 

Bypass air injected into the aft mixing chamber has an 
effect on the regression rate upstream in the fuel grain. 
At high pressures and low air mass flux rates, the principal 
mechanism for wall heat flux became radiation, and resulted 
in the regression rate becoming insensitive to G. For PMM, 
regression rate takes the form: 

.42 .003 
r = .001 16P G 

While Known to be advantageous with ail-hydrocarbon 
fuels, the use of bypass air flow with fuels containing 
oxygen (or those which decompose into monomers or small 
hydrocarbon molecules) appears to slow the kinetics of the 
combustion process and lower performance. Fuels containing 



33 



their own oxidizer or substances to unzip the hydrocarbon 
chain show definite possibilities for high performance and 
an alternative to the use of bypass systems. 

With the use of bypass systems, it is possible to set up 
not only combustor-f eed system type oscillations but also 
instabilities dependent on the effect of the^bypass flew on 
the combustion process within the aft mixing chamber and on 
the fuel regression rate. 



34 



VII. SUGGESTIONS FOR FUTURE WORK 



Additional experimental studies are required to better 
understand the internal ballistics of the aft mixing section 
of the solid fuel ramjet. In the area of bypass systems, 
more work is needed in studying the combustion process ahead 
of and behind the aft mixing chamber reattachment point. 
Specific experimental studies should include: a) aft dump 
flow rates and momentum, b) alternate fuels, c) the effect 
of axial position of the aft dumps and d) the use of longer 
mixing sections to allow more time for complete combustion, 
with a consideration of the tradeoff between added weight 
and increased efficiency. Experimental and analytical work 
are required on the feasibility of developing a solid fuel 
ramjet fuel which will supply the necessary performance 
characteristics for use in a propulsion system without the 
need for bypass. 



35 




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51 



APPENDIX B 



THEORETICAL PERFORMANCE FOR PMM-AIR 



Equations for the calculation of the equilibrium gas 
constant (f t-lbf/lbm-°R) , ratio of specific heats, and 
combustion temperature (°F) as a fuction of inlet 
temperature (°R) , combustion pressure (psia) and air-fuel 
ratio for Polymethylmethacrylate and air. 

Pc =50 Ti = 500 

R = 85.9609 + af * (-8.7617 + af *(0.7589 -0.0215 * af ) ) 

g = 1.449S14 + af *(-0. 059068 + af *(0. 0055187 - 0.0001566 * 

af)) 

T = 503.7493 + af *(180.1897 + af *(141.7147 + af * (-20. 1361 

+ 0.7044 * af))) 

Pc = 100 Ti = 500 

R = 86.0584 + af *(-8.7582 + af *(0.7585 - 0.0214 * af)) 

g = 1.43718 + af *(-0. 053096 + af *(0. 004661 - 0.0001187 * 

af)) 

T = 7272.9547 + af *(-3858.64 + af *(991.307 + af *(-95.2704 

+ 3.0781 * af) ) ) 

Pc =50 Ti = 750 

R = 85.7005 + af *(-3.6698 ♦ af *(0.7506 - 0.0213 * af ) ) 

g = 1.440205 + af *(-0. 056445 + af *(0. 00528 - 0.00015 * 

af)) 

T = 95.53247 + af *(439.4649 + af *(30.676 + af *(-15.1934 + 

0.56511 * af ) ) ) 

Pc = 100 Ti = 750 

R = 85.8749 + af *(-8.7313 + af *(0.7561 - 0.0215 * af)) 

g = 1.44198 + af * (-0 . 057074 + af *(0. 005337 - 0.000152 * 



52 



af)) 

T = 397.6427 + af *(308.8051 + af *(117.7353 + af *(-18.2495 
+ 0.6523 * af})) 

Pc =50 Ti = 1000 

B = 85.4012 + af *(-8.565 + af *(0.7416 - 0.0211 * af )) 

g = 1.430833 + af *(-0. 053936 + af * (0 . 005058 - 0.0001449 * 

af)) 

T = 501.175 + af *(364.7408 + af *(99.204 + af *(-16.202 + 

0.582 * af ) ) ) 

Pc = 100 Ti = 1000 

R = 86.0304 + af *(-8.8284 + af *(0.7739 - 0.0224 * af)) 

g = 1.42658 + af *(-0. 05177 + af *(0. 0047196 - 0.0001292 * 

af)) 

T = 4721.969 + af *(-2203.3985 + af * (651.37 12 + af 

*(-66.083 + 2. 1875 * af) ) ) 



53 



LIST OF REFERENCES 

1. Holzman, A.L. , Experimental Studies of Combustion 
Processes in Solid Fueled Ramjets , presented at JANNAF 
Workshop on SFRJ, Naval Postgraduate School, June 8-10, 
1976. 

2. Naval Postgraduate School Report 57NT73091B, An 
Investigation of the Internal Ballistics of Solid Fuel 
Ramjets : A Progress Report , by L. D. Boaz, C. E. 
Jones III and D. W. Netzer, September 1973. 

3. Naval Postgraduate School Report 57NT73031A, An 
Investigation of the Internal Ballistics of Solid Fuel 
Ramj ets , p. 1-6, by L. D. Boaz and D. W. Netzer, March 
1973. 

4. Holzman, A. L. , Personal Communication, June 1976. 

5. Schadow, K.C., Experimental Studies of Combustion 
Processes in Solid Fueled Ramjets , presented at JANNAF 
Workshop on SFRJ, Naval Postgraduate School, June 8-10, 
1976. 

6. Bulban, E.J., "Light Rocket Features Solid-Fuel 
Ramjet", Aviation Week, p. 87-90, July 31, 1961. 

7. Naval Postgraduate School Report 57NT74081, Flow 
Characteristics in Solid Fuel Ramjets, p. 52, by J.T. 
Phaneuf, Jr. and D. W. Netzer, July 1974. 



54 



8. McVey, J.3., Recommended Ramburner Test Reporting 
Standards, p. 6-7, CPIA Publication No. 276, March 
1976. 

9. Hoi man, J. P., Experimental Methods for Engineers, p. 
37 r 40, Mcgraw-Hill, 1966. 

10. Schadow, K.C., Forbes, H.F. and Chiese, D.J., 
"Experimental Studies of Combustion Processes in Solid 
Fueled Ramjets", Thirteenth JANNAF Combustion Meeting, 
CPIA Publication No. 281, Vol. Ill, p. 245-259, 
December 1976. 



55 



INITIAL DISTRIBUTION LIST 



No. Copies 

1. Defense Documentation Center 2 

Cameron Station 
Alexandria, Virginia 22314 

I. Library, Code 0142 2 

Naval Postgraduate School 
Monterey, California 93940 

3. Department Chairman, Code 67 1 

Department of Aeronautics 
Naval Postgraduate School 
Monterey, California 93940 

I. Assoc. Professor D. H. Netzer, Code 67Nt 3 

Department of Aeronautics 
Naval Postgraduate School 
Monterey, California 93940 

3. IT C. J. Mady, Jr. , USN 1 

135 5 N. Van Ness Avenue 
Fresno, California 93728 

6. Dean of Research 1 

Naval Postgraduate School 
Monterey, CA 93940 



56 



f 

Thesi g 
M27488 
c.l 



131851 

Mady 

Effect of configura- 
tion variables on per- 
formance of sol id fuel 

ramjets. 



Thesi s 
M27488 
c.l 



Mady ^ f 1851 

Effect of configura- 
tion variables on per- 
formance of solid fuel 

ramjets. 



thesM27488 

E !!, e , Ct ° f conf| 9uration variables 





on per 



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